In a wide-ranging policy address on Tuesday, Cantor backed the principles behind the DREAM Act, which would grant legal status and a path to citizenship to young immigrants who were brought to the U.S. illegally as children by their parents.

“One of the great founding principles of our country was that children would not be punished for the mistakes of their parents,” Cantor said in his speech. “It is time to provide an opportunity for legal residence and citizenship for those who were brought to this country as children and who know no other home.”

The legislation was a top Democratic priority as recently as two years ago, but after President Obama offered protection from deportation for many so-called “dreamers” in 2012 through executive action, the party has shifted to a push for a comprehensive immigration overhaul.

Speaking at the party’s annual retreat about an hour’s drive from Washington, Becerra said “it’s great that our Republican colleagues are catching up,” but he insisted they go further. “So I hope that they’re going to put on fast forward on the Republican side when it comes to dealing with immigration reform,” Becerra said. “If the playing field for them is, ‘DREAM Act is a good idea,’ that’s yesterday’s news.”

While the DREAM Act is expected to be included in any broad reform, the caucus vice chairman, Rep. Joseph Crowley (N.Y.), said the president’s action last year had largely resolved the issue. “The heavy-lifting was done by the president, and somehow my Republican colleagues want to take credit for what was done already,” he said.

Still, both Becerra and Crowley said they were encouraged by the willingness of Republican leaders to consider more comprehensive reform. The Democrats had a panel on the issue on Wednesday, and it is expected to be a prime topic of discussion throughout their retreat.